Finite Group Databasebeta

← C2×#83996 #11670327

Subgroups — C2×#83996 #11670327

Order 768.

2742 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#137C211yesmaximal, characteristic, complemented
2C2×#5824C211yesmaximal, characteristic
3C2×Q8×#67C211yesmaximal, characteristic, complemented
4C22×#915C211yesmaximal, characteristic, complemented
5C2×#5239C211yesmaximal, characteristic, complemented
6C2×#5228C211yesmaximal, characteristic, complemented
7#83996C2116yesmaximal, direct product factor
8C2×#5189C211yesmaximal, characteristic, complemented
9C2×#5186C211yesmaximal, characteristic, complemented
10C2×#5183C211yesmaximal, characteristic, complemented
11C2×#5182C211yesmaximal, characteristic, complemented
12C2×#5173C211yesmaximal, characteristic, complemented
13C2×#5162C211yesmaximal, characteristic, complemented
14C2×Dic3×SD16C211yesmaximal, characteristic, complemented
15C2×#5137C211yesmaximal, characteristic, complemented
16C2×#5128C211yesmaximal, characteristic, complemented
17C2×#3276—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic
19C23×C3×Q8C2211yescharacteristic
20C22×D3×Q8C2211yescharacteristic
21C22×#237C2211yescharacteristic
22C2×C3×#137—28no—
23C2×C3×#137C2218yescomplemented
24C22×C3×Q16C2211yescharacteristic
25C22×C3×Q16C2211yescharacteristic
26C22×C3×SD16C2211yescharacteristic
27C22×C3×SD16C2211yescharacteristic
28C22×C3×M16C2211yescharacteristic
29#5824—24no—
30#5824C2218yes—
31Q8×#67—24no—
32Q8×#67C2218yescomplemented
33C2×#946—21no—
34C2×#946C2211yescharacteristic
35C2×#946C2211yescharacteristic
36C2×Q8×Dic3C2211yescharacteristic
37C2×#944—21no—
38C2×#944C2211yescharacteristic
39C2×#944C2211yescharacteristic
40C22×#216C2211yescharacteristic
41C22×#216C2211yescharacteristic
42C22×#216C2211yescharacteristic
43C2×#939—21no—
44C2×#935—21no—
45C2×D4×Dic3C2211yescharacteristic
46C22×#214C2211yescharacteristic
47C2×#929—21no—
48C2×C4×#67—21no—
49C2×C4×#67C2211yescharacteristic
50C2×#924—21no—
51C2×#924C2211yescharacteristic
52C2×#924C2211yescharacteristic
53C22×Dic3⋊C4—21no—
54C2×#915—28no—
55C2×#915C2218yescomplemented
56C22×Dic12C2211yescharacteristic
57C22×ΓL(1,𝔽25)C2211yescharacteristic
58#5239C2218yescomplemented
59#5228C2218yescomplemented
60C2×#835C2211yescharacteristic
61C2×#835C2211yescharacteristic
62C2×#835C2211yescharacteristic
63C2×#832C2211yescharacteristic
64C2×#830C2211yescharacteristic
65#5189C2218yescomplemented
66#5186C2218yescomplemented
67#5183C2218yescomplemented
68#5182C2218yescomplemented
69#5173C2218yescomplemented
70#5162C2218yescomplemented
71Dic3×SD16C2218yescomplemented
72#5137C2218yescomplemented
73#5128C2218yescomplemented
74C2×(C2×D3)⋊C8C2211yescharacteristic
75C2×#817C2211yescharacteristic
76C2×#816C2211yescharacteristic
77C2×#816C2211yescharacteristic
78C2×Dic3⋊C8C2211yescharacteristic
79C2×C8×Dic3C2211yescharacteristic
80C22×#137—31no—
81C22×#137D311yescharacteristic, complemented
82C2×D4×Q8—31no—
83C2×#547—31no—
84#3276—316no—
85C2×#494—31no—
86C2×#470—31no—
87C2×#470—31no—
88C2×#462—31no—
89C2×#461—31no—
90C2×#452—31no—
91C2×#452—31no—
92C2×#451—31no—
93C2×#451—31no—
94C2×C4×SD16—31no—
95C2×#436—31no—
96C2×C3×#41—22no—
97C2×C3×#41—24no—
98C2×C3×#41—42no—
99C2×C3×#41C2314yes—
100C22×C3×Q8—21no—
101C22×C3×Q8—22no—
102C22×C3×Q8—24no—
103C22×C3×Q8—42no—
104C22×C3×Q8C2311yescharacteristic
105C22×C3×Q8C2311yescharacteristic
106C22×C3×Q8C2314yes—
107C22×C3×Q8C2311yescharacteristic
108C22×C3×D4—21no—
109C22×C3×D4C2311yescharacteristic
110C23×C3×C4—21no—
111C23×C3×C4—21no—
112C23×C3×C4C2311yescharacteristic
113C22×#67—21no—
114C22×#67D411yescharacteristic
115C23×Dic3—21no—
116C23×Dic3—21no—
117C2×D3×Q8—22no—
118C2×D3×Q8—24no—
119C2×D3×Q8—42no—
120C2×D3×Q8C2314yes—
121C2×#237—24no—
122C2×#237—22no—
123C2×#237—42no—
124C2×#237C2314yes—
125C22×C4×D3—21no—
126C22×C4×D3C2311yescharacteristic
127C22×Dic6—21no—
128C22×Dic6C2311yescharacteristic
129C22×Dic6C2311yescharacteristic
130C3×#137—232no—
131C2×C3×Q16—24no—
132C2×C3×Q16—24no—
133C2×C3×Q16C2314yes—
134C2×C3×Q16C2314yes—
135C2×C3×SD16—24no—
136C2×C3×SD16D418yescomplemented
137C2×C3×SD16C2314yes—
138C2×C3×SD16C2314yes—
139C2×C3×M16—24no—
140C2×C3×M16C2314yes—
141C22×C3×C8C2311yescharacteristic
142C22×C3×C8C2311yescharacteristic
143C2×#217—21no—
144C2×#217—21no—
145C2×#217—21no—
146C2×#217D411yescharacteristic
147#946—22no—
148#946—22no—
149#946—28no—
150#946C2314yes—
151#946C2314yes—
152Q8×Dic3—22no—
153Q8×Dic3C2314yes—
154#944—28no—
155#944—22no—
156#944—22no—
157#944C2314yes—
158#944C2314yes—
159C2×#216—24no—
160C2×#216—42no—
161C2×#216—42no—
162C2×#216C2314yes—
163C2×#216C2314yes—
164C2×#216C2314yes—
165#939—28no—
166#935—28no—
167D4×Dic3—22no—
168D4×Dic3C2314yes—
169C2×#214—24no—
170C2×#214C2314yes—
171#929—28no—
172C4×#67—28no—
173C4×#67D414yes—
174C4×#67C2314yes—
175C2×(C2×D3)⋊C4—21no—
176C2×(C2×D3)⋊C4—21no—
177C2×(C2×D3)⋊C4D411yescharacteristic
178C2×C4⋊Dic3—21no—
179C2×C4⋊Dic3C2311yescharacteristic
180C2×C4⋊Dic3C2311yescharacteristic
181#924—22no—
182#924—22no—
183#924—28no—
184#924C2314yes—
185#924C2314yes—
186C2×Dic3⋊C4—21no—
187C2×Dic3⋊C4—21no—
188C2×Dic3⋊C4—21no—
189C2×Dic3⋊C4—21no—
190C2×Dic3⋊C4—21no—
191C2×Dic3⋊C4—21no—
192C2×Dic3⋊C4—21no—
193C2×Dic3⋊C4—21no—
194C2×Dic3⋊C4—28no—
195C2×Dic3⋊C4D411yescharacteristic
196C2×C4×Dic3—21no—
197C2×C4×Dic3C2311yescharacteristic
198C22×C3⋊C8C2311yescharacteristic
199C22×C3⋊C8C2311yescharacteristic
200#915—232no—
201C2×Dic12—24no—
202C2×Dic12C2314yes—
203C2×ΓL(1,𝔽25)—24no—
204C2×ΓL(1,𝔽25)C2314yes—
205#835C2314yes—
206#835C2314yes—
207#835C2314yes—
208#832C2314yes—
209#830C2314yes—
210(C2×D3)⋊C8C2314yes—
211#817C2314yes—
212#816C2314yes—
213#816C2314yes—
214Dic3⋊C8C2314yes—
215C8×Dic3C2314yes—
216C22×#41—31no—
217C22×#41C2×D311yescharacteristic
218C23×Q8—31no—
219C23×Q8C2×D311yescharacteristic
220C2×#137—28no—
221C2×#137—38no—
222C2×#137—68no—
223C2×#137C2×D318yescomplemented
224C22×Q16—31no—
225C22×Q16—31no—
226C22×Q16—31no—
227C22×Q16—31no—
228C22×Q16C2×D311yescharacteristic
229C22×Q16C2×D311yescharacteristic
230C22×SD16—31no—
231C22×SD16C2×D311yescharacteristic
232C22×SD16C2×D311yescharacteristic
233C22×M16—31no—
234C22×M16C2×D311yescharacteristic
235D4×Q8—38no—
236D4×Q8—64no—
237#547—38no—
238#547—64no—
239C2×C4⋊Q8—31no—
240C2×C4⋊Q8—31no—
241C2×C4⋊Q8—61no—
242C2×#123—61no—
243C2×#123—61no—
244C2×C22⋊Q8—31no—
245C2×C22⋊Q8—31no—
246C2×C22⋊Q8—31no—
247C2×C22⋊Q8—31no—
248C2×C22⋊Q8—61no—
249C2×C22⋊Q8—61no—
250C2×#121—61no—
251C2×C4×Q8—31no—
252C2×C4×D4—31no—
253C2×C4×D4—31no—
254C2×C4×D4—61no—
255C22×C4⋊C4—61no—
256#494—38no—
257#470—38no—
258#470—38no—
259#462—38no—
260#461—38no—
261#452—38no—
262#452—38no—
263#451—38no—
264#451—38no—
265C4×SD16—38no—
266#436—38no—
267C2×#106—31no—
268C2×C4⋊C8—31no—
269C2×#103—31no—
270C2×#103—31no—
271C2×#103—31no—
272C2×#103—31no—
273C2×#103—31no—
274C2×#102—31no—
275C2×C22⋊C8—31no—
276C2×C22⋊C8—31no—
277C2×C4×C8—31no—
278C24×C3—21no—
279C24×C3C2×D411yescharacteristic
280C23×D3C2×D411yescharacteristic
281C3×#41—28no—
282C3×#41—44no—
283C3×#41—48no—
284C2×C3×Q8—21no—
285C2×C3×Q8—24no—
286C2×C3×Q8—21no—
287C2×C3×Q8—21no—
288C2×C3×Q8—22no—
289C2×C3×Q8—28no—
290C2×C3×Q8—22no—
291C2×C3×Q8—22no—
292C2×C3×Q8—22no—
293C2×C3×Q8—22no—
294C2×C3×Q8—44no—
295C2×C3×Q8—44no—
296C2×C3×Q8—48no—
297C2×C3×Q8C2×D414yes—
298C2×C3×Q8C2412yes—
299C2×C3×Q8C2412yes—
300C2×C3×Q8C2412yes—
301C2×C3×D4—24no—
302C2×C3×D4—21no—
303C2×C3×D4—22no—
304C2×C3×D4—44no—
305C2×C3×D4C2×D414yes—
306C2×C3×D4C2412yes—
307C22×C3×C4—21no—
308C22×C3×C4—22no—
309C22×C3×C4—22no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—24no—
313C22×C3×C4—24no—
314C22×C3×C4—44no—
315C22×C3×C4—44no—
316C22×C3×C4C2×D411yescharacteristic
317C22×C3×C4C2×D412yes—
318C22×C3×C4C2412yes—
319C22×C3×C4C2411yescharacteristic
320C2×#67—24no—
321C2×#67—24no—
322C2×#67—44no—
323C2×#67C2×D414yes—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—24no—
329C22×Dic3—24no—
330C22×Dic3—44no—
331C22×Dic3—44no—
332C22×Dic3C2×D411yescharacteristic
333C22×Dic3C2×D411yescharacteristic
334C22×Dic3C2×D411yescharacteristic
335D3×Q8—28no—
336D3×Q8—44no—
337D3×Q8—48no—
338#237—28no—
339#237—44no—
340#237—48no—
341C2×C4×D3—22no—
342C2×C4×D3—22no—
343C2×C4×D3—24no—
344C2×C4×D3—44no—
345C2×C4×D3C2×D412yes—
346C2×C4×D3C2412yes—
347C2×Dic6—22no—
348C2×Dic6—22no—
349C2×Dic6—22no—
350C2×Dic6—22no—
351C2×Dic6—21no—
352C2×Dic6—21no—
353C2×Dic6—24no—
354C2×Dic6—44no—
355C2×Dic6C2412yes—
356C2×Dic6C2412yes—
357C3×Q16—28no—
358C3×Q16—28no—
359C3×SD16—28no—
360C3×SD16C2×D4116yescomplemented
361C3×M16—28no—
362C2×C3×C8—22no—
363C2×C3×C8C2×D414yes—
364C2×C3×C8C2412yes—
365C2×C3×C8C2412yes—
366#217—24no—
367#217—24no—
368#217—24no—
369#217C2×D414yes—
370#216—28no—
371#216—44no—
372#216—44no—
373#214—28no—
374(C2×D3)⋊C4—24no—
375(C2×D3)⋊C4—24no—
376(C2×D3)⋊C4C2×D414yes—
377C4⋊Dic3—21no—
378C4⋊Dic3—21no—
379C4⋊Dic3—24no—
380C4⋊Dic3C2412yes—
381C4⋊Dic3C2412yes—
382Dic3⋊C4—24no—
383Dic3⋊C4—24no—
384Dic3⋊C4—24no—
385Dic3⋊C4—24no—
386Dic3⋊C4—24no—
387Dic3⋊C4—24no—
388Dic3⋊C4—24no—
389Dic3⋊C4—24no—
390Dic3⋊C4C2×D414yes—
391C4×Dic3—24no—
392C4×Dic3C2×D412yes—
393C4×Dic3C2412yes—
394C2×C3⋊C8—22no—
395C2×C3⋊C8—22no—
396C2×C3⋊C8C2412yes—
397C2×C3⋊C8C2412yes—
398Dic12—28no—
399ΓL(1,𝔽25)—28no—
400C2×#41—22no—
401C2×#41—24no—
402C2×#41—34no—
403C2×#41—42no—
404C2×#41—62no—
405C2×#41—64no—
406C2×#41—122no—
407C2×#41C22×D314yes—
408C22×Q8—21no—
409C22×Q8—22no—
410C22×Q8—24no—
411C22×Q8—34no—
412C22×Q8—31no—
413C22×Q8—31no—
414C22×Q8—42no—
415C22×Q8—61no—
416C22×Q8—62no—
417C22×Q8—64no—
418C22×Q8—122no—
419C22×Q8C22×D311yescharacteristic
420C22×Q8C22×D311yescharacteristic
421C22×Q8C22×D314yes—
422C22×Q8C22×D311yescharacteristic
423C22×D4—21no—
424C22×D4—31no—
425C22×D4—61no—
426C22×D4C22×D311yescharacteristic
427C23×C4—21no—
428C23×C4—21no—
429C23×C4—31no—
430C23×C4—61no—
431C23×C4—61no—
432C23×C4—61no—
433C23×C4C22×D311yescharacteristic
434#137—232no—
435#137—632no—
436C2×Q16—24no—
437C2×Q16—24no—
438C2×Q16—34no—
439C2×Q16—34no—
440C2×Q16—34no—
441C2×Q16—34no—
442C2×Q16—64no—
443C2×Q16—64no—
444C2×Q16—122no—
445C2×Q16—122no—
446C2×Q16C22×D314yes—
447C2×Q16C22×D314yes—
448C2×SD16—24no—
449C2×SD16—34no—
450C2×SD16—64no—
451C2×SD16#6718yescomplemented
452C2×SD16C22×D314yes—
453C2×SD16C22×D314yes—
454C2×M16—24no—
455C2×M16—34no—
456C2×M16—64no—
457C2×M16C22×D314yes—
458C22×C8—31no—
459C22×C8—31no—
460C22×C8C22×D311yescharacteristic
461C22×C8C22×D311yescharacteristic
462C4⋊Q8—34no—
463C4⋊Q8—34no—
464C4⋊Q8—62no—
465C4⋊Q8—62no—
466C4⋊Q8—68no—
467#123—68no—
468#123—68no—
469C22⋊Q8—34no—
470C22⋊Q8—34no—
471C22⋊Q8—34no—
472C22⋊Q8—34no—
473C22⋊Q8—68no—
474C22⋊Q8—68no—
475C22⋊Q8—62no—
476C22⋊Q8—62no—
477C22⋊Q8—62no—
478C22⋊Q8—62no—
479#121—68no—
480C4×Q8—34no—
481C4×Q8—62no—
482C4×D4—34no—
483C4×D4—34no—
484C4×D4—34no—
485C4×D4—62no—
486C4×D4—68no—
487C2×C4⋊C4—31no—
488C2×C4⋊C4—31no—
489C2×C4⋊C4—31no—
490C2×C4⋊C4—68no—
491C2×C4⋊C4—61no—
492C2×C4⋊C4—61no—
493C2×C4⋊C4—61no—
494C2×C4⋊C4—61no—
495C2×C4⋊C4—61no—
496C2×C4⋊C4—61no—
497C2×C4⋊C4—61no—
498C2×C4⋊C4—61no—
499C2×C4⋊C4—61no—
500C2×C22⋊C4—31no—
501C2×C22⋊C4—31no—
502C2×C22⋊C4—61no—
503C2×C22⋊C4—61no—
504C2×C22⋊C4—61no—
505C2×C22⋊C4—61no—
506C2×C22⋊C4—61no—
507C2×C42—31no—
508C2×C42—61no—
509#106—34no—
510C4⋊C8—34no—
511#103—34no—
512#103—34no—
513#103—34no—
514#103—34no—
515#103—34no—
516#102—34no—
517C22⋊C8—34no—
518C22⋊C8—34no—
519C4×C8—34no—
520C23×C3—24no—
521C23×C3—22no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—42no—
526C23×C3—42no—
527C23×C3C22×D412yes—
528C23×C3C22×D411yescharacteristic
529C22×D3—22no—
530C22×D3—22no—
531C22×D3—22no—
532C22×D3C22×D412yes—
533C3×Q8—24no—
534C3×Q8—22no—
535C3×Q8—22no—
536C3×Q8—22no—
537C3×Q8—22no—
538C3×Q8—22no—
539C3×Q8—48no—
540C3×Q8—42no—
541C3×Q8—42no—
542C3×Q8C22×D414yes—
543C3×D4—24no—
544C3×D4—22no—
545C3×D4—48no—
546C3×D4C22×D414yes—
547C2×C3×C4—24no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—24no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—48no—
556C2×C3×C4—48no—
557C2×C3×C4—42no—
558C2×C3×C4—42no—
559C2×C3×C4C22×D412yes—
560C2×C3×C4C22×D411yescharacteristic
561C2×C3×C4C22×D412yes—
562C2×C3×C4H(5,𝔽2)12yes—
563C2×C3×C4C2511yescharacteristic
564#67—28no—
565#67—48no—
566C2×Dic3—22no—
567C2×Dic3—22no—
568C2×Dic3—22no—
569C2×Dic3—22no—
570C2×Dic3—22no—
571C2×Dic3—22no—
572C2×Dic3—48no—
573C2×Dic3—42no—
574C2×Dic3—42no—
575C2×Dic3—42no—
576C2×Dic3—42no—
577C2×Dic3—48no—
578C2×Dic3#13714yescomplemented
579C2×Dic3C22×D412yes—
580C2×Dic3C22×D412yes—
581C2×Dic3C22×D412yes—
582C4×D3—24no—
583C4×D3—22no—
584C4×D3—22no—
585C4×D3—48no—
586Dic6—22no—
587Dic6—22no—
588Dic6—22no—
589Dic6—22no—
590Dic6—48no—
591Dic6—42no—
592Dic6—42no—
593C3×C8—22no—
594C3×C8C22×D414yes—
595C3⋊C8—22no—
596C3⋊C8—22no—
597C24—21no—
598C24—31no—
599C24D3×D411yescharacteristic
600#41—28no—
601#41—44no—
602#41—48no—
603#41—68no—
604#41—124no—
605#41—128no—
606C2×Q8—21no—
607C2×Q8—24no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—22no—
611C2×Q8—28no—
612C2×Q8—22no—
613C2×Q8—22no—
614C2×Q8—22no—
615C2×Q8—22no—
616C2×Q8—32no—
617C2×Q8—32no—
618C2×Q8—44no—
619C2×Q8—44no—
620C2×Q8—48no—
621C2×Q8—64no—
622C2×Q8—61no—
623C2×Q8—61no—
624C2×Q8—68no—
625C2×Q8—62no—
626C2×Q8—62no—
627C2×Q8—62no—
628C2×Q8—62no—
629C2×Q8—124no—
630C2×Q8—124no—
631C2×Q8—128no—
632C2×Q8C2×#6714yes—
633C2×Q8C23×D312yes—
634C2×Q8C23×D312yes—
635C2×Q8C23×D312yes—
636C2×D4—24no—
637C2×D4—21no—
638C2×D4—22no—
639C2×D4—34no—
640C2×D4—44no—
641C2×D4—64no—
642C2×D4—64no—
643C2×D4—124no—
644C2×D4C2×#6714yes—
645C2×D4C23×D312yes—
646C22×C4—21no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—24no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—24no—
653C22×C4—31no—
654C22×C4—31no—
655C22×C4—31no—
656C22×C4—32no—
657C22×C4—32no—
658C22×C4—44no—
659C22×C4—44no—
660C22×C4—64no—
661C22×C4—64no—
662C22×C4—64no—
663C22×C4—62no—
664C22×C4—62no—
665C22×C4—61no—
666C22×C4—61no—
667C22×C4—61no—
668C22×C4—61no—
669C22×C4—124no—
670C22×C4—124no—
671C22×C4—124no—
672C22×C4D3×D412yes—
673C22×C4D3×D411yescharacteristic
674C22×C4C23×D312yes—
675C22×C4C23×D311yescharacteristic
676Q16—28no—
677Q16—28no—
678Q16—68no—
679Q16—68no—
680Q16—124no—
681Q16—124no—
682SD16—28no—
683SD16—68no—
684SD16C2×#67116yescomplemented
685M16—28no—
686M16—68no—
687C2×C8—22no—
688C2×C8—32no—
689C2×C8—32no—
690C2×C8—62no—
691C2×C8—62no—
692C2×C8C2×#6714yes—
693C2×C8C23×D312yes—
694C2×C8C23×D312yes—
695C4⋊C4—34no—
696C4⋊C4—32no—
697C4⋊C4—32no—
698C4⋊C4—64no—
699C4⋊C4—64no—
700C4⋊C4—64no—
701C4⋊C4—64no—
702C4⋊C4—64no—
703C4⋊C4—64no—
704C4⋊C4—64no—
705C4⋊C4—61no—
706C4⋊C4—61no—
707C4⋊C4—64no—
708C4⋊C4—64no—
709C22⋊C4—34no—
710C22⋊C4—34no—
711C22⋊C4—64no—
712C22⋊C4—64no—
713C22⋊C4—64no—
714C22⋊C4—64no—
715C22⋊C4—64no—
716C42—32no—
717C42—32no—
718C42—64no—
719C22×C3—24no—
720C22×C3—22no—
721C22×C3—22no—
722C22×C3—22no—
723C22×C3—44no—
724C22×C3—48no—
725C22×C3—42no—
726C22×C3—42no—
727C22×C3D4212yes—
728C22×C3C2×#13712yes—
729C22×C3#57812yes—
730C22×C3C23×D411yescharacteristic
731C2×D3—22no—
732C2×D3—22no—
733C2×D3—22no—
734C2×D3—44no—
735C3×C4—24no—
736C3×C4—22no—
737C3×C4—42no—
738C3×C4—42no—
739C3×C4D4212yes—
740C3×C4C23×D411yescharacteristic
741C3×C4C2×H(5,𝔽2)11yescharacteristic
742Dic3—22no—
743Dic3—22no—
744Dic3—42no—
745Dic3—42no—
746Dic3—42no—
747Dic3—42no—
748Dic3C2×#13714yescomplemented
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—24no—
754C23—32no—
755C23—42no—
756C23—42no—
757C23—62no—
758C23—62no—
759C23—62no—
760C23C2×D3×D412yes—
761C23C2×D3×D411yescharacteristic
762Q8—22no—
763Q8—24no—
764Q8—22no—
765Q8—22no—
766Q8—22no—
767Q8—22no—
768Q8—48no—
769Q8—42no—
770Q8—42no—
771Q8—62no—
772Q8—62no—
773Q8—62no—
774Q8—62no—
775Q8—128no—
776Q8—122no—
777Q8—122no—
778Q8C22×#6714yes—
779D4—22no—
780D4—24no—
781D4—48no—
782D4—68no—
783D4—128no—
784D4C22×#6714yes—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—24no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—24no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—32no—
794C2×C4—34no—
795C2×C4—32no—
796C2×C4—32no—
797C2×C4—48no—
798C2×C4—48no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—62no—
802C2×C4—62no—
803C2×C4—62no—
804C2×C4—62no—
805C2×C4—64no—
806C2×C4—62no—
807C2×C4—62no—
808C2×C4—62no—
809C2×C4—62no—
810C2×C4—128no—
811C2×C4—128no—
812C2×C4—128no—
813C2×C4—122no—
814C2×C4—122no—
815C2×C4—122no—
816C2×C4—122no—
817C2×C4C2×D3×D412yes—
818C2×C4C2×D3×D411yescharacteristic
819C2×C4#100412yes—
820C2×C4C22×#6712yes—
821C2×C4C24×D311yescharacteristic
822C8—22no—
823C8—62no—
824C8—62no—
825C8C22×#6714yes—
826C2×C3—42no—
827C2×C3—44no—
828C2×C3#327614yescomplemented
829C2×C3C2×D4211yescharacteristic
830C2×C3C22×#13711yescharacteristic
831C2×C3C2×#57811yescharacteristic
832D3—42no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—24no—
837C22—44no—
838C22—48no—
839C22—42no—
840C22—42no—
841C22—62no—
842C22—62no—
843C22—62no—
844C22—124no—
845C22D3×#13712yes—
846C22#577912yes—
847C22D4×#6712yes—
848C22C22×D3×D411yescharacteristic
849C4—22no—
850C4—24no—
851C4—34no—
852C4—42no—
853C4—42no—
854C4—62no—
855C4—62no—
856C4—122no—
857C4—122no—
858C4—122no—
859C4—122no—
860C4D4×#6712yes—
861C4C2×#100411yescharacteristic
862C4C23×#6711yescharacteristic
863C3C2×#327611yescharacteristic, complemented, Sylow
864C2—42no—
865C2—44no—
866C2—122no—
867C2#8399614yesdirect product factor
868C2C2×D3×#13711yescharacteristic
869C2C2×#577911yescharacteristic
870C2C2×D4×#6711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC22×C3×#137C2
socleC23×C3C22×D4
prime radicalC2×#5824C2
hypercenterC22×#137D3
hypocenterC3C2×#3276
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×C3×#137C2semidirect
3. C2×Q8×#67C2semidirect
4. C22×#915C2semidirect
5. C2×#5239C2semidirect
6. C2×#5228C2semidirect
7. #83996C2direct (N × H)
8. C2×#5189C2semidirect
9. C2×#5186C2semidirect
10. C2×#5183C2semidirect
11. C2×#5182C2semidirect
12. C2×#5173C2semidirect
13. C2×#5162C2semidirect
14. C2×Dic3×SD16C2semidirect
15. C2×#5137C2semidirect
16. C2×#5128C2semidirect
23. C2×C3×#137C22semidirect
32. Q8×#67C22semidirect
55. C2×#915C22semidirect
58. #5239C22semidirect
59. #5228C22semidirect
65. #5189C22semidirect
66. #5186C22semidirect
67. #5183C22semidirect
68. #5182C22semidirect
69. #5173C22semidirect
70. #5162C22semidirect
71. Dic3×SD16C22semidirect
72. #5137C22semidirect
73. #5128C22semidirect
81. C22×#137D3semidirect
136. C2×C3×SD16D4semidirect
223. C2×#137C2×D3semidirect
360. C3×SD16C2×D4semidirect
451. C2×SD16#67semidirect
578. C2×Dic3#137semidirect
684. SD16C2×#67semidirect
748. Dic3C2×#137semidirect
828. C2×C3#3276semidirect
863. C3C2×#3276semidirect
867. C2#83996direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C3×#1372
C2×#58242
C2×Q8×#672
C22×#9152
C2×#52392
C2×#52282
#839962
C2×#51892
C2×#51862
C2×#51832
C2×#51822
C2×#51732
C2×#51622
C2×Dic3×SD162
C2×#51372
C2×#51282
C2×#32763